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Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H-atom is suitable for this purpose? [R_H = 1 × 10⁵ cm⁻¹, h = 6.6 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s]

1. Balmer, ∞ → 2
2. Paschen, 5 → 3
3. Paschen, ∞ → 3
4. Lyman, ∞ → 1

Correct answer: Paschen, ∞ → 3

Solution

For Paschen series limit (infinity -> 3): 1/lambda = R_H/9 = (1e5 cm^-1)/9, giving lambda = 9e-5 cm = 900 nm. So the suitable line is Paschen, infinity -> 3. (Balmer infinity -> 2 gives 400 nm.)

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